Preheat your oven to 375°F (190°C). Bring a large pot of salted water to a boil and cook the penne pasta according to package instructions, usually about 9-11 minutes, until al dente. Drain and set aside.
In a large mixing bowl, whisk together the Greek yogurt, softened cream cheese, crumbled feta, garlic powder, onion powder, dried oregano, salt, and pepper. Stir until smooth and creamy.
Add the cooked shredded chicken, chopped spinach, cherry tomatoes, sliced olives, and cooked pasta into the bowl with the sauce. Gently fold everything together until the pasta is well coated and the veggies and chicken are evenly distributed.
Drizzle the olive oil into your baking dish and spread the pasta mixture evenly. Sprinkle the shredded mozzarella cheese over the top.
Bake uncovered for 20-25 minutes or until the cheese is bubbly and lightly golden. Remove from the oven and let it cool for a few minutes before serving.